FIG. 1 illustrates a conventional prior-art butterfly 10, including first and second input terminals 11 and 12, respectively, and first and second output terminals 21 and 22. Signals applied to first input terminal 11 are coupled to noninverting input ports of summing circuits (summers) 14 and 15. Signals applied to second input terminal 12 are weighted in a multiplier 13 with a weight W.sup.K, and the resulting weighted signal is applied to a further noninverting input port of summing circuit 14, and to an inverting input port of summing circuit 15. Summing circuit 14 sums the signal from first input terminal 11 with the weighted signal to produce an output signal on first output terminal 21. Summing circuit 15 subtracts the weighted signal from the signal applied to input terminal 11 to produce an output signal on second output terminal 22.
FIG. 2 illustrates a typical prior-art eight-point Fast Fourier Transform (FFT) architecture 30 in a conventional representation. In the representation of FIG. 2, each butterfly, corresponding to 10 of FIG. 1, is illustrated as a pair of crossed lines. One such pair of crossed lines 32, 34 is identified by a dash-line rectangular surround designated 10. Each butterfly of FIG. 2 bears a marking in the form W.sup.K adjacent to the lower left crossed line, where ##EQU1## The indicated value of W.sup.K is applied in FIG. 2 to the multiplier, corresponding to multiplier 13 of FIG. 1, which is associated with each butterfly.
The FFT structure of FIGS. 2 takes advantage of computational redundancies in the Discrete Fourier Transform (DFT) to reduce the total number of computations required to produce the filtered output signal. In radar applications, one of the primary uses of the FFT is in pulse Doppler filtering, in which it effectively performs the function of a bank of narrow-band filters, each tuned to a different Doppler frequency, to thereby separate or sort radar returns or echoes according to the velocities of the targets. This ability to sort by the target velocity, in turn, is valuable in that it allows suppression of signals relating to stationary or slowly-moving targets (clutter), thereby making fast-moving targets such as aircraft more obvious. The input signals applied to the Pulse 1, Pulse 2; Pulse 3...Pulse 8 input ports of FFT architecture 30 of FIG. 2 are range traces from a succession of transmitted pulses; i.e. the echo occurring at a particular time
(corresponding to a particular range) after transmission of each of eight successive pulses. Thus, the signals applied to the FFT 30 input ports are "windowed", in that they represent a finite number (eight) sequential samples out of an indefinite number of samples. Those skilled in the art know that such windowing can result in undesirable sidelobes in the system output. These sidelobes, in the Doppler filter context, result in cross-coupling of signals among the filters. The cross-coupling means that the signal at the output of each filter, which ideally represents only those returns from targets moving at a particular velocity, will be contaminated by return signals "leaking" from other Doppler frequencies. When attempting to detect a moving target (an incoming missile) in the presence of large, slowly moving clutter (moving waves, in a maritime context), the sidelobes may allow the clutter to obscure the target. It is very important to detect missiles as early as possible, so that time remains after detection in which countermeasures may be taken. Conventional FFT Doppler filters, therefore, are designed with very low sidelobe levels, but the concomitants of low sidelobe levels are (a) a relatively wide frequency bandwidth, and (b) high losses compared with high sidelobe designs. The relatively wide bandwidth in turn means that mutually adjacent filters overlap each frequency, so that returns from a particular target appear in the outputs of plural filters, and the target velocities therefore can only be generally determined.
The sidelobe levels of the filters formed by the FFT structure of FIG. 2 using the butterflies of FIG. 1 can be controlled by applying a weighting function to the windowed data applied to input ports designated Pulse 1-Pulse 8; such weighting functions generally attenuate the signals at the ends of the windows (the Pulse 1 and Pulse 8 input ports) relative to the signals near the center of the window (the Pulse 4 and Pulse 5 input ports). For example, in high Clutter Improvement Factor (CIF) applications in which ultra-low sidelobes are required, an 85-dB Dolph-Chebychev window weighting function can be used. Such a weighting applied to an FFT structure similar to that of FIG. 2, but with 16 points instead of eight points, results in the response illustrated in FIG. 3, in which the sidelobes are uniformly 85 dB below the filter peak response. FIG. 3 plots amplitude-versus-normalized-frequency response from each of the sixteen output ports of a sixteen-point FFT structure, superposed upon each other. The illustrated plot has 33 separate peaks, two for each of the sixteen filters except the zero-frequency filter, which displays a peak at a normalized Doppler frequency of zero, and a peak at normalized frequencies of +1 and -1. Each filter, other than the zero-frequency filter, exhibits a peak in the positive Doppler frequency region and another in the negative region at a distance of 1 normalized doppler interval from the positive peak, e.g. the filter which peaks at 0.8 also peaks at -0.2. The filter responses illustrated in FIG. 3 are normalized to an amplitude of zero dB, which represents a filter loss of 2.5 dB at the peak of the response. The filter responses are also relatively broad, with a null to null bandwidth equal to 0.4 of Doppler space.
In many cases, clutter may be concentrated at particular frequencies, as for example clutter due to wind motion of vegetation and wave motion at sea tends to be at very low Doppler frequencies. It would be desirable to be able to provide the filters of an FFT Doppler filter bank with suppression at particular frequencies at which clutter is known to occur, while using low-loss, relatively narrow bandwidth filters at other frequencies.